Statistics Activity 1: Rolling Dice Simulation

Transcription

1 Statistics Activity 1: Rolling Dice Simulation Kathleen Mittag Keystrokes for the Calculator From the Main Menu, press for STAT. If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow) Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the random number data in List 1 and List. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1(List 1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Create a Histogram: In the STAT mode Press F1 (GRPH) F4 (SEL). Make sure Graph 1 is turned on. Then press EXIT. Press F6 (SET). Press down arrow key to Graph Type. Press F6. Then press F1 for Histogram. Press down arrow key to Xlist, press F1. Press down arrow key and F1 (1). Press EXIT F1 for Graph 1. Set the start and pitch at 1. Then press EXE and the graph should appear. To trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then MENU. Press F1 to change Stat Window to Auto. Statistics Activity 1: Rolling Dice Simulation 1

2 Name Date Statistics Activity 1: Rolling Dice Simulation Student Worksheet Activity 1 Before using a graphing calculator, complete a table of possible outcomes from rolling two dice. Remember that an outcome of,4 is different from an outcome of 4, even though the sums are the same. There are 36 possible outcomes. To simulate the rolling of a pair of dice: In the RUN mode, press OPTN F6 F4 F EXIT F3 ( F ) then EXE. This will give you one random integer between 1 and 6, inclusive. Press EXE again and again to generate more values. Complete the table below by entering 5 random integers between 1 and 6, inclusive, into the calculator in List 1 then repeat for 5 more random integers for List using the STAT mode as explained at the end of the activity. L1 L Now you can add corresponding values in List 1 and List and put the sum in List 3 by using the calculator. In the STAT mode, highlight List 3, press OPTN F1 F1 1 + OPTN F1 F1 EXE. To graphically view the sums, you need to graph a histogram as explained at the end of the activity. Sketch the histogram below: Complete the frequency table below: L L Then answer the following questions using the data above: Statistics Activity 1: Rolling Dice Simulation

3 Name Date Student Worksheet Activity 1 1. What is the experimental probability of a 7?. What is the experimental probability of a 7 or 11? (Pass line bet wins in craps) 3. What is the experimental probability of a, 3, or a 1? (Pass line bet loses in craps) Next using theoretical probability, answer the following questions. 4. What is the probability of a 7? 5. What is the probability of a 7 or 11? (Pass line bet wins in craps) 6. What is the probability of a, 3, or a 1? (Pass line bet loses in craps) Now combine data from three other students to complete the following table. L L Using the data above (n =100), answer questions What is the experimental probability of a 7? 8. What is the experimental probability of a 7 or 11? (Pass line bet wins in craps) 9. What is the experimental probability of a, 3, or a 1? (Pass line bet loses in craps) How do the answers for 1-3 compare to the answers for 7-9? How do they each compare to the theoretical probabilities in answers 4-6. Statistics Activity 1: Rolling Dice Simulation 3

4 Statistics Activity : Gender Probability Activity Kathleen Mittag Keystrokes for the Calculator From the Main Menu, press for STAT. If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow) Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the random number data in List 1 and List. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1(List1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Create a Histogram: In the STAT mode Press F1 (GRPH) F4 (SEL). Make sure Graph 1 is turned on. Then press EXIT. Press F6 (SET). Press down arrow key to Graph Type. Press F6. Then press F1 for Histogram. Press down arrow key to Xlist, press F1. Press down arrow key and F1 (List1). Press EXIT F1 for Graph 1. Set the start and pitch at 1. Then press EXE and the graph should appear. To trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then MENU. Press F1 to change Stat Window to Auto. Statistics Activity : Gender Probability Activity 1

5 Name Date Statistics Activity : Gender Probability Activity Student Worksheet Activity Traditionally, people believe that the probability of having a girl baby or a boy baby is equal with each being 50%. In reality, the answer is the probability of a boy is which is 51.3%. To simulate the gender of a baby, generate random numbers that will be either 1 or. Allow girls to be 1 and boys to be. In the RUN mode, press OPTN F6 F4 F EXIT F3 ( F4 + 1 ) then EXE. This will give you one random integer between 1 and, inclusive. Generate 50 random numbers and enter them into the table below. Enter the data into the calculator in List 1 using the STAT mode as explained at the end of the activity. To view the data, graph a histogram as explained at the end of the activity. Sketch the histogram below: Answer the following questions: 1. What is the experimental probability of having a girl?. What is the experimental probability of having a boy? 3. What is the experimental probability of having a girl or a boy? Statistics Activity : Gender Probability Activity

6 Name Date Student Worksheet Activity 4. What is the experimental probability of having a girl and a boy? 5. What is the experimental probability of having a girl then having a boy? 6. What is the experimental probability of having 5 girls and no boys? 7. What is the experimental probability of at least one girl if a woman has 3 children? Gather the data for the entire class: Number of boys: Number of girls: Total number of trials: Answer questions 1-7 using the class data: Statistics Activity : Gender Probability Activity 3

7 Name Date Student Worksheet Activity Answer questions 1-7 using the theoretical probability that the birth or a boy or girl is equally likely: How do your experimental, the class and the theoretical probabilities compare? Explain. Statistics Activity : Gender Probability Activity 4

8 Statistics Activity 3: Birthday Problem Kathleen Mittag Keystrokes for the Calculator From the Main Menu, press for STAT. If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow) Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the random number data in List 1 and List. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1(List 1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Create a Histogram: In the STAT mode Press F1 (GRPH) F4 (SEL). Make sure Graph 1 is turned on. Then press EXIT. Press F6 (SET). Press down arrow key to Graph Type. Press F6. Then press F1 for Histogram. Press down arrow key to Xlist, press F1. Press down arrow key and F1 (1). Press EXIT F1 for Graph 1. Set the start and pitch at 1. Then press EXE and the graph should appear. To trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then MENU. Press F1 to change Stat Window to Auto. Statistics Activity 3: Birthday Problem 1

9 Name Date Statistics Activity 3: Birthday Problem Student Worksheet Activity 3 A classical statistics probability problem is "What is the probability of having at least two people with the same birthday (day and month, not year) in a group?" The theoretical probabilities by size of group are quite easy to calculate and will surprise many people. To begin, you do an easier example by asking "What is the probability of two people being born during the same month?" You know that if there are 13 people then there must be at least two born during the same month. To calculate the probability of at least two born during the same month from a group with 4 people, first the number of birth month possibilities is 1 4 =0,736. The number of possibilities of not any having the same birth month is the permutation of 1 taken 4 at a time (P(1,4)) which is: 1! = 11,880 8! The number of possibilities of at least two birthdays in the same month would be: 0,736 11,880 = 8856 Then probability of at least two birthdays in the same month would be: 8856/0736 = 0.47 This easier example can be used to derive a general equation for at least having the same birth date from a group with size g. Probability of at least two people having the same birth date month from a group of g people is: (Use 1 if calculating same month or 365 if calculating same date.) Pr(g) = 1g or 1! (1 g)! 1 g Pr(g) = 365g (365 g + 1) 365 g 1. Use this formula to calculate the probability of at least two people being born in the same month from a group of 6 people. Statistics Activity 3: Birthday Problem

10 Name Date Student Worksheet Activity 3 Complete the following table by calculating the probabilities of at least two people being born the same day of the year from groups of size, 10, 5, 30 and 60. Group Size Probability People are really surprised by these results since with a group of only 5 people you have a 57% chance of two having the same birthday. Graph the above data as a scatterplot and sketch the scatterplot below. Calculate the best fit regression equation for this graph. Compare this regression equation to the probability equation given earlier in the lesson using 365 days. Statistics Activity 3: Birthday Problem 3

11 Statistics Activity 3: Birthday Problem continued Teacher Note The answers for problem are: Group Size Probability <1% 10 1% 5 57% 30 71% 60 99% Statistics Activity 3: Birthday Problem 4

12 Statistics Activity 4: One-Variable Descriptive Statistics, Box Plot and Outliers Keystrokes for the Calculator From the Main Menu, press for STAT. Kathleen Mittag and Sharon Taylor If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow). Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the grade data in List 1. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1 (List1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Create a Box plot: Press EXIT twice. Press F1 (GRPH) then F6 (SET). Press down arrow key to Graph Type, press F6, then press F for MedBox. Press down arrow key to XList then press F1 (List1). Press EXIT F1 for Graph 1. To Trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then MENU. Press F1 to change Stat Window to Auto. Statistics Activity 4: One-Variable Descriptive Statistics, Box Plot and Outliers 1

13 Name Date Statistics Activity 4: One-Variable Descriptive Statistics, Box Plot and Outliers Student Worksheet Activity 4 The following data were the daily grades for a Calculus I class a) Find the following: Mean= Median= Mode: Interpret these measures of central tendency. b) Find the following: Standard deviation for sample = Range = Interpret these measures of dispersion. c) Find the five values needed for to graph the Box Plot. Minimum = Q1 = Median = Q3= Maximum = d) Sketch the Box Plot below: e) Determine mathematically if there are any outliers and identify the outliers if applicable. Discuss reasons why or why not there are outliers. Statistics Activity 4: One-Variable Descriptive Statistics, Box Plot and Outliers

14 Statistics Activity 5: One-Variable Data with Histogram Keystrokes for the Calculator From the Main Menu, press for STAT. Kathleen Mittag and Sharon Taylor If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow). Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the accident data in List 1. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1 (List1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Create a Histogram: Press EXIT twice. Press F1 (GRPH) then F6 (SET). Press down arrow key to Graph Type, press F6, then press F1 for Histogram. Press down arrow key to XList then press F1 (List1). Press EXIT F1 for Graph 1. Statistics Activity 5: One-Variable Data with Histogram 1

15 Statistics Activity 5: One-Variable Data with Histogram continued Keystrokes for the Calculator You will be shown a Set Interval screen. Start the interval with the minimum numerical value of the data set. Pitch is determined by how wide you want to set each interval. For this data set let pitch be 1 first for 9 intervals then be for 5 intervals. To Trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then MENU. Press F1 to change Stat Window to Auto. Create a xy line (which is also called a connected point line): Press EXIT twice. Enter a new data list into List. This data will be the numbers Press F1 (graph) then F6 (set). Press down arrow key to Graph Type then press F for xy. Press down arrow key to XList then press F (List ). Press down arrow key to YList then press F1 (List 1). Press EXIT F1 for Graph 1. Statistics Activity 5: One-Variable Data with Histogram

16 Name Date Statistics Activity 5: One-Variable Data with Histogram Student Worksheet Activity 5 The following data set is the number of fender-bender automobile accidents reported per day during a recent month at a local discount store in a large city. Sunday Monday Tuesday Wednesday Thursday 1 Friday Saturday a) Calculate and interpret the one-variable statistics for the data. Mean= Median= Mode: Interpret these measures of central tendency. Standard deviation for sample = Range = Interpret these measures of dispersion. Minimum = Q1 = Median = Q3= Maximum = b) Construct a histogram showing 9 intervals and another histogram showing 5 intervals then sketch both histograms below. Statistics Activity 5: One-Variable Data with Histogram 3

17 Name Date Statistics Activity 5: One-Variable Data with Histogram Student Worksheet Activity 5 c) What do the histograms show? d) How can the histograms be used to interpret the data? e) Now sketch a connected point line plot by plotting the numbers 1-30 on the x-axis and the data set on the y-axis. f) What does the line plot reveal about the data set? Statistics Activity 5: One-Variable Data with Histogram 4

18 Statistics Activity 6: One-Variable Descriptive Statistics Keystrokes for the Calculator From the Main Menu, press for STAT. Kathleen Mittag and Sharon Taylor If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow). Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the waiting time data in List 1. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (CALC) then F6 (SET). With 1-Var Xlist highlighted, press F1 (List1). Press F1 (1-VAR). Use the down arrow key to scroll for more values. Statistics Activity 6: One-Variable Descriptive Statistics 1

19 Name Date Statistics Activity 6: One-Variable Descriptive Statistics Student Worksheet Activity 6 The following data are minutes waiting in the 0 items or less checkout line at a local grocery store.: a) Calculate and interpret the one-variable statistics for the data. Mean= Median= Mode: Interpret these measures of central tendency. Standard deviation for sample = Standard deviation for the population = Range = Interpret these measures of dispersion. Statistics Activity 6: One-Variable Descriptive Statistics

20 Statistics Activity 8 Scatterplots-Quadratic From the Main Menu, press for STAT. If there are data in List 1 and List, follow these directions: Press F6 (make sure that the highlighted cell is in List 1 by pressing the right/left/up/down arrow). Press F4 (DEL-A) then press F1 (YES). Repeat this process for List if necessary. Enter Data: Type the average speed data in List 1 With appropriate cell highlighted, type numerical value then EXE to store. Use the right arrow key to go over to List and then type in the miles per gallon data. Make sure your data is matched up correctly and that you have 10 entries in both List 1 and List. Graph the scatterplot: Press F6 (more) and then Press F1 (GRPH). Press F6 (SET) to set up your graph. Press down arrow key to Graph Type, press F1 (Scat). Press down arrow key to XList then press F1 (List1). Press down arrow key to Ylist then press F (List). The frequency should be 1 and you can choose the type of mark you would like to make. Press EXIT and then F1 for Graph 1. To get the line of best fit: Press F3 (x^) to find a quadratic regression model. To see the line of best fit with the data: Press F6 (DRAW). Keystrokes for the Calculator Kathleen Mittag and Sharon Taylor Statistics Activity 8: Scatterplots-Quadratic 1

21 Name Date Statistics Activity 8: Scatterplots-Quadratic Student Worksheet Activity 8 An engineer is interested in finding out about how average speed influences the miles per gallon a car gets. Her data for a particular car is in the table below. Average Speed (mph) Miles Per Gallon (mpg) Enter the data into your calculator.. Graph the scatterplot. 3. Describe the shape of the data. 4. Explain in everyday language and in terms of the problem what is happening. 5. Use your calculator to find an equation that fits the data. a. What equation will fit best? b. Why did you make this choice? c. What did you see in the data that influenced your decision? Statistics Activity 8: Scatterplots-Quadratic

22 Statistics Activity 9 Scatterplots-Exponential From the Main Menu, press for STAT. If there are data in List 1 and List, follow these directions: Press F6 (make sure that the highlighted cell is in List 1 by pressing the right/left/up/down arrow). Press F4 (DEL-A) then press F1 (YES). Repeat this process for List if necessary. Enter Data: Type the week data in List 1 With appropriate cell highlighted, type numerical value then EXE to store. Use the right arrow key to go over to List and then type in the weight data. Make sure your data is matched up correctly and that you have 7 entries in both List 1 and List. Graph the scatterplot: Press F1 (GRPH) then F6 (SET) Press down arrow key to Graph Type, press F1. Press down arrow key to XList then press F1 (List1). Press down arrow key to Ylist then press F (List). The frequency should be 1 and you can choose the type of mark you would like to make. Press EXIT and then F1 for Graph 1. To get the line of best fit: Press F6 (more options) and then press F (Exp) to find an exponential regression line To see the line of best fit with the data: Press F6 (DRAW). Keystrokes for the Calculator Kathleen Mittag and Sharon Taylor Statistics Activity 9: Scatterplots-Exponential 1

23 Name Date Statistics Activity 9: Scatterplots-Exponential Student Worksheet Activity 9 Radioactive materials decay at a certain rate. Each material has its own rate of decay. These rates are computed by collecting data and then analyzing them. A scientist begins with a 100-gram sample and the weighs the sample each week. Data from the measurements of a certain radioactive material are listed in the table below. Week Weight (in grams) Enter the data into your calculator.. Graph the scatterplot. 3. Describe the pattern that you see. 4. Look at the data in the table. Between which two measurements was there exactly half of the original sample left? 5. Use your calculator to compute the exponential regression for this data. 6. In a perfect situation, the coefficient should be 100. Is it? If so, explain why. If not, explain why. 7. The base of the exponent explains the rate of decay. What is that rate? What does that mean in everyday language? 8. Graph the line y = 50. Find the point of intersection with this line and the exponential equation. How does this compare to your answer for #4? Statistics Activity 9: Scatterplots-Exponential

24 Statistics Activity: Central Limit Theorem Simulation Kathleen Mittag Teaching Notes and Answers An easy way to simulate the Central Limit Theorem is to use the last four digits of student social security numbers. Do this by writing each of the ten digits (0-9) on the board and have students come to the board and put a check under each of the digits that are in the last four digits of their social security number. If a digit appears more than once in their number, just put more than one check. This method retains confidentiality. You will need at least 30 students to have this work properly. The first boxplot (social security numbers) should be a uniform distribution and the second boxplot (last 4 digit means) should be a normal distribution. Then have each student calculate the mean of the last four digits of his/her social security number and record all the means in List 1 of your graphing calculator. Answers to the Problems: Answers will vary depending on data. The student social security number simulation should produce a uniform distribution The means should produce a normal distribution and the mean and standard deviation of the means should be very close to the Central Limit Theorem values. Central Limit Theorem Simulation 1

25 Name Date Central Limit Theorem Simulation Student Worksheet The Central Limit Theorem (CLT) is essential for inferential statistics but difficult for students to understand. The CLT is: The Central Limit Theorem states that if n is sufficiently large, the sample means of random samples from a population with mean m and finite standard deviation s are approximately normally distributed with mean m and standard deviation. n An easy way to simulate the CLT is to use the last four digits of student social security numbers. Your teacher will write the ten digits (0-9) on the board. Each students will go to the board and put a check under each of the digits that are in the last four digits of his or her social security number. If a digit appears more than once in their number, just put more than one check. Then fill in the table below with the total number for each digit. Digit # of Digits 1. Sketch and label the graph of the boxplot to the right with minimum, Q1, median, Q3, and maximum. Use the calculator.. What does the distribution appear to be? Now calculate the mean of the last four digits of your social security number and record all the means in List 1 of your graphing calculator. 3. Sketch and label the graph of the boxplot at the right with minimum, Q1, median, Q3, and maximum. Use the calculator. 4. What does the distribution appear to be? 5. Use the calculator to calculate the mean and standard deviation of the data used for questions 3 and 4. Compare these values to the CLT. Central Limit Theorem Simulation

26 Statistics Activity: Central Limit Theorem Simulation Kathleen Mittag Keystrokes for the Calculator From the Main Menu, press for STAT. If there are data in List 1, follow these directions: Press F6 (make sure that the highlighted cell is List 1 by pressing the right/left arrow). Press F4 (DEL-A) then press F1 (YES). Enter Data: Type the data in List 1. With appropriate cell highlighted, type numerical value then EXE to store. Find One-Variable Statistics: Press F (calculate) then F6 (set). With 1Var Xlist highlighted, press F1. Press F1 (1VAR). Use the down arrow key to scroll for more values. Create a Boxplot: In the STAT mode Press EXIT. Press F1 (GRPH), F4 (make sure Graph 1 is turned on) then press EXIT. Press F6 (SET). Press down arrow key to Graph Type, F6 then press F for Median Boxplot then EXE. Press down arrow key to Xlist, press F1(List 1), then set the frequency to 1. Press EXIT, F1 for Graph 1 and the graph should appear. To Trace, press SHIFT F1. If your graph does not appear, follow these directions: Press SHIFT then SETUP. Press F1 to change Stat Window to Auto. Central Limit Theorem Simulation 3

27 Hypothesis Testing for Two Sample CALCULATORS: Casio: fx-9750g Plus Casio: CFX-9850G Series Kathleen Mittag Student Handout A hypothesis test is conducted when trying to find out if a claim is true or not. And if the claim is true, is it significant. The calculator makes hypothesis testing easier by performing the computations. After inputting the data that you have for a problem, the calculator will give you a p-value. The relationship between the p-value and the given level of significance for the problem will determine your decision. If p < a, then you will reject the null hypothesis. If p > a, then you will fail to reject the null hypothesis. Hypothesis testing for the -sample mean for large independent samples uses a z-test. You will need to have the following information for the hypothesis test: the null hypothesis the alternative hypothesis (this will tell you if you are using a one-sided or two-sided test) the means of each of the sample data sets the standard deviations of each of the sample data sets. The number in each sample. Problem: Every year you do an activity using plain M&M candies. You are interested in determining of the mean weight of the candies changes from one year to the next. The first year you sampled 100 M&M candies and found that the mean weight was grams and the standard deviation was grams. The next year you sampled 100 M&M candies and found that the mean weight was grams and the standard deviation was grams. Is the difference between the two sample means significant? Answer: The z test statistic is and the p-value is Since the p-value is greater than 0.05, you fail to reject the null hypothesis and conclude that there is not enough evidence to consider the two samples different. Using the Calculator In the main menu, press (STAT). Press F3(TEST). (It does not matter if data is in lists.) Press F1(Z). Press F(-S). Choose Var for Data. For this problem, choose. Enter the standard deviations, means and sample sizes for the two samples of M&Ms. With Execute highlighted, press F1(CALC). The answer will appear. Hypothesis Testing for Two Sample 1

28 Name Date Confidence Intervals for Means of Two Large Independent Samples CALCULATORS: Casio: fx-9750g Plus Casio: CFX-9850G Series Student Worksheet Kathleen Mittag Confidence Interval is an interval of values computed from sample data that is likely to include the true population value. If we consider all possible randomly selected samples of the same size from a population, the confidence level is the fraction or percent of those samples for which the confidence interval includes the population parameter. Common confidence levels are 80%, 90%, 95% and 99%. Problems: Every year you do an activity using plain M&M candies. You are interested in determining of the mean weight of the candies changes from one year to the next. The first year you sampled 100 M&M candies and found that the mean weight was grams and the standard deviation was grams. The next year you sampled 100 M&M candies and found that the mean weight was grams and the standard deviation was grams. Is the difference between the two sample means significant? 1. Let s look at how the confidence intervals change width for the same sample data as the confidence level changes. Use the M&M data sets. a) Calculate the 80% confidence interval. b) Calculate the 90% confidence interval. c) Calculate the 95% confidence interval. d) Calculate the 99% confidence interval. e) What is happening to the widths of the intervals as the confidence level increases? Why do you think this is occurring?. Do you think there is a difference between the sample means? Explain your answer. Confidence Intervals for Means of Two Large Independent Samples 1

29 Confidence Intervals for Means of Two Large Independent Samples CALCULATORS: Casio: fx-9750g Plus Casio: CFX-9850G Series Kathleen Mittag Keystrokes and Answers Using the Calculator In the main menu, press (STAT). Press F4(INTR). (It does not matter if data is in lists.) Press F1(Z). Press F(-S). Choose Var for Data. Enter the confidence level,.8 for 80%. Enter the standard deviations, means and sample sizes for the two samples of M&Ms. With Execute highlighted, press F1(CALC). The answer will appear. Answers: 1. a) < ( 1 - ) < This interval contains zero so it is likely that the two population means are equal. b) < ( 1 - ) < This interval contains zero so it is likely that the two population means are equal. c) < ( 1 - ) < This interval contains zero so it is likely that the two population means are equal. d) < ( 1 - ) < This interval contains zero so it is likely that the two population means are equal. e) The intervals get wider as the confidence level gets more accurate. This makes sense since as you get more precise the interval will be wider because of sampling error.. There confidence intervals indicate that there is likely no difference between the sample means. Confidence Intervals for Means of Two Large Independent Samples

30 Confidence Intervals for Means of Two Large Independent Samples 3